Sex Education: Need of the Hour

Sex education, despite the everlasting force of modernisation in other regards, has remained a contentious issue, especially in India. This short note attempts to briefly explore the history of sexuality and how societal perspectives and expectations have evolved with time. The importance of sex education and sensitisation cannot go ignored for much longer. This paper makes reference to the recommendations of prominent international organisations and makes recommendations of its own, all with the objective of limiting stigma and precipitating sexual/reproductive welfare.

On the Counter-Rotation of Closed Time-like Curves

While it is tempting to think of closed time-like curves (CTCs) around rotating bodies, such as a black hole, as being “caused” by the rotation of the source, Andréka et al. pointed out that the underlying physics are not as straightforward as this, since such CTCs are “counter-rotating”, i.e., the time orientation (the opening of the local light cones) of the CTCs is opposite to the direction in which the singularity or the ergosphere rotates. It was also suggested that this is a generic phenomenon that calls for a deeper intuitive physical understanding. In this short note, we point out—with Kerr–Taub–NUT as an example—that CTCs are counter-rotating with respect to the local angular velocity of the spacetime, not the global angular momentum, nor the angular velocity of the black hole horizon, which makes the physical interpretation of CTCs being “caused” by a rotating source even more problematic.

Short Note on the Riemann Hypothesis

Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n)<e^{\gamma }\times n \times\log\log n$ holds for all natural numbers $n>5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$ and $\gamma\approx0.57721$ is the Euler-Mascheroni constant. Let $q_{1}=2,q_{2}=3,\ldots,q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m}q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n>5040$ such that Robin inequality does not hold and we prove that $n^{\left(1-\frac{0.6253}{\log q_{m}}\right)}<N_{m}$, where $N_{m}=\prod_{i =1}^{m}q_{i}$ is the primorial number of order $m$ and $q_{m}$ is the largest prime divisor of $n$. In addition, we show that $q_{m}$ will not have an upper bound by some positive value for these counterexamples and therefore, the value of $q_{m}$ tends to infinity as $n$ goes to infinity.

Short Note on the Riemann Hypothesis

Robin criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n)<e^{\gamma }\times n \times\log\log n$ holds for all natural numbers $n>5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$ and $\gamma\approx0.57721$ is the Euler-Mascheroni constant. Let $q_{1}=2,q_{2}=3,\ldots,q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m}q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n>5040$ such that Robin inequality does not hold and we prove that $n^{\left(1-\frac{0.6253}{\log q_{m}}\right)}<N_{m}$, where $N_{m}=\prod_{i =1}^{m}q_{i}$ is the primorial number of order $m$ and $q_{m}$ is the largest prime divisor of $n$. In addition, we show that $q_{m}$ will not have an upper bound by some positive value for these counterexamples and therefore, the value of $q_{m}$ tends to infinity as $n$ goes to infinity.

First generic record of aero-terrestrial algae Apatococcus lobatus (Chodat) J.B.Petersen for algal flora of Nepal

Short note

Short Note: Rape A Consequence of Covid-19 Quarantine on Children and The Elderly: A Call for Action

The novel coronavirus (Covid-19) led to a shift in the social structure of global cities leading to self-isolation and social/physical distancing to curb the spread of the virus. While these two are stand as good policy, they are greeted by domestic violence and rape as the most prevalent consequences. The researchers examined the impact of lockdown on domestic violence in Nigeria based on frequency of news reports using content analysis of two online news reports and discovered a high prevalence of rape on children (0 - 17 years) and elderly (60 years and above). Hence it is suggested that the government should always be prepared for emergencies. Also, future polices should consider the interest of the most vulnerable in the society by providing safety measures.

A short note on the BMI and on secular changes in BMI

Human size changes over time with worldwide secular trends in height, weight, and body mass index (BMI). There is general agreement to relate the state of nutrition to height and weight, and to ratios of weight-to-height. The BMI is a ratio. It is commonly used to classify underweight, overweight and obesity in adults. Yet, the BMI is inappropriate to provide any immediate information on body composition. It is accepted that the BMI is “a simple index to classify underweight, overweight and obesity in adults”. It is stated that “policies, programmes and investments need to be “nutrition-sensitive”, which means they must have positive impacts on nutrition”. It is also stated that “a need for policies that address all forms of malnutrition by making healthy foods accessible and affordable, while restricting unhealthy foods through fiscal and regulatory restrictions“. But these statements are neither warranted by arithmetic considerations, nor by historic evidence. Measuring the BMI is an appropriate screening tool for detecting an unusual weight-to-height ratio, but the BMI is an inappropriate tool for estimating body composition, or suggesting medical and health policy decisions.

The Origin of the Name ‘Mongol’

This short note proposes that a hapax legomenon in a fifth century list of enemies of Khotan might give a half a millennium antecedent to the name of the Mongols, as an alternative, and older, name of the Mongol-speaking Rouran.